Question

DF=
Help me please:))​

Answer 1

`\fbox {DF = 20}`

Explanation:

Given :

• ΔSDF ~ ΔRTY = 4 : 9 (Ratio of similitude)
• SF = RT - 2
• TY = RY + 9
• SD = 8

Step 1 : Find RT

• SD : RT = 4 : 9
• 8 : RT = 4 : 9
• RT = 18

Step 2 : Find SF

• SF = RT - 2
• SF = 18 - 2
• SF = 16

Step 3 : Find RY

• SF : RY = 4 : 9
• 16 : RY = 4 : 9
• RY = 36

Step 4 : Find TY

• TY = RY + 9
• TY = 36 + 9
• TY = 45

Step 5 : Find DF

• DF : TY = 4 : 9
• DF : 45 = 4 : 9
• DF = 20

Answer 2

DF = 20

Explanation:

Triangle SDF has side lengths SD, DF, SF.

Triangle RTY has side lengths

RT = (9/4)SD

RY = (9/4)SF

TY = (9/4)DF

"SF is 2 less than RT" Given

SF = RT - 2

SF = (9/4)SD - 2

"SD = 8" Given

SF = (9/4)(8) - 2

SF = 16

"TY is 9 more than RY" Given

TY = RY + 9

(9/4)DF = (9/4)SF + 9

(9/4)DF = (9/4)(16) + 9

(9/4)DF = 45

DF = 45 × 4/9

DF = 20